Gravitational fields of local cosmic strings
75
"tII''''
Figure 3.4. Conical singularity on the space outside a local cosmic string. 0 is the axis of
the string.
between 2:n-(l-4GNIL) and 2:n- removed. In addition, because 0 = 0 and 0 = 2:nare to be identified, we must identify fJ = 0 and fJ = 2:n- - 60 where
60;;;: 8:n-GNIL.
(3.52)
Then, looking along the z-axis, space looks as in figure 3.4 with the hatched area
removed and points at the same value of p on the dotted lines identified. The
conical singularity in the space outside a long straight local cosmic string has
several striking consequences:
3.5.1 Double images [5]
A galaxy located behind a local cosmic string, from the perspective of the
observer, will acquire a double image. Consider, for simplicity, an infinitely
long straight cosmic string nonnal to the plane of the page in figure 3.5 with
the observer cv and the galaxy g being observed in the plane of the page. Because
points A and B are identified, as discussed earlier, two images of the galaxy are
seen, emanating from A and B. The angle between the two images 6a is given
by
d16a = d260
(3.53)
where dl and d2 are, respectively, the distances from the observer to the galaxy
and from the cosmic string to the galaxy. As a consequence of (3.52),
d2
6a = d) 8:n-GNIL·
(3.54)